N(x, y) = xy Step 2 The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = taN(x, y). M(tx, ty) = -(ty)³ + (tx)³ -) (-x³ + x³) M(x, y) = N(tx, ty) = (tx) (ty)² )(xy2) xy² N(X, Y) Therefore, the equation is homogeneous where a =
N(x, y) = xy Step 2 The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = taN(x, y). M(tx, ty) = -(ty)³ + (tx)³ -) (-x³ + x³) M(x, y) = N(tx, ty) = (tx) (ty)² )(xy2) xy² N(X, Y) Therefore, the equation is homogeneous where a =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer step 2 ty.
![Step 1
We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0.
Find the functions M and N.
M(x, y) =
N(x, y) =
xy² dy - (³x³) dx = 0
xy2 dy + (-y³ + x³) dx = 0
xy²
xy² dx = y³ – x³
xy2 dy = (y3x³) dx
N(tx, ty) = (tx) (ty)²
Step 2
The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = N(x, y).
M(tx, ty) = -(ty)³ + (tx)³
)c-v3 +
M(x, y)
73
)(xy²)
ry²
+ x³)
N(x, y)
Therefore, the equation is homogeneous where a =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb52044d-d588-4d60-8413-960f544d05a0%2F36622768-1409-4949-9d9a-8063ce36e7bd%2F1lgmez6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Step 1
We are given a differential equation and will rewrite it in the form M(x, y) dx + N(x, y) dy = 0.
Find the functions M and N.
M(x, y) =
N(x, y) =
xy² dy - (³x³) dx = 0
xy2 dy + (-y³ + x³) dx = 0
xy²
xy² dx = y³ – x³
xy2 dy = (y3x³) dx
N(tx, ty) = (tx) (ty)²
Step 2
The equation M(x, y) dx + N(x, y) dy = 0 is said to be homogeneous if there is a real number a such that M(tx, ty) = M(x, y) and N(tx, ty) = N(x, y).
M(tx, ty) = -(ty)³ + (tx)³
)c-v3 +
M(x, y)
73
)(xy²)
ry²
+ x³)
N(x, y)
Therefore, the equation is homogeneous where a =
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